Here is the documentation.
I interpret the doc to say that covariates are internally centered and scaled during the LASSO process. However, the final parameter estimates are provided for the original variables.
If you want to run the experiment, you could use PROC STDIZE to standardize your regressors and run the program twice, once on the original data and once on the standardized data. The selected effects should be the same. I did a similar experiment in the article "Standardized regression coefficients."